This paper is devoted to the game theoretic analysis of decision situations, in which the players have veto power over the actions undertaken by certain other players. We give a full characterization of the dividends in these games with a permission structure. We find that the collection of these games forms a subspace of the vector space of all games with side payments on a specified player set.Two applications of these results are provided. The first one deals with the projection of additive games on a permission structure. It is shown that the Shapley value of these projected games can be interpreted as an index that measures the power of the players in the permission structure. The second application applies the derived results on games, where the organization structure can be analysed separately from the production capacities of the participating players.

The aim of this paper is to introduce cooperative games with a feasible coalition system which is called antimatroid. These combinatorial structures generalize the permission structures, which have nice economical applications. With this goal, we …rst characterize the approaches from a permission structure with special classes of antimatroids. Next, we use the concept of interior operator in an antimatroid and we de…ne the restricted game taking into account the limited possibilities of cooperation determined by the antimatroid. These games extend the restricted games obtained by permission structures. Finally, we provide a computational method to obtain the Shapley and Banzhaf values of the players in the restricted game, by using the worths of the original game.

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ABSTRACT. A situation, in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (point-valued) solution for TU-games assigns a payoff distribution to every TU-game. In this article we discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS-value, the ENSC-value and the equal division solution. We provide several characterizations of this class of solutions on variable and fixed player set. Specifications of several properties characterize specific solutions in this class.

In this paper we provide an axiomatization of the Shapley value for TUgames using a fairness property. This property states that if to a game we add another game in which t w o players are symmetric then their payo s change by the same amount. We show that the Shapley value is characterized by this fairness property, e ciency and the null player property. These three axioms also characterize the Shapley value on important subclasses of games, such a s the class of simple games or the class of apex games.

One of the main issues in economic allocation problems is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide three different characterizations of egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, from the perspective of a variable player set, we show that all these solutions satisfy the same reduced game consistency. Second, on a fixed player set, we characterize this class of solutions using monotonicity properties. Finally, towards a strategic foundation, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game. These characterizations discover fundamental differences as well as intriguing connections between marginalism and egalitarianism. R. van den Brink (B)

A situation in which players can generate certain pay-offs by cooperating can be described by a coopemtive gnme with transferable utililies. In this paper we assume that the players who are participating in such a game, are part of some permission structure. This means that there are players who need permission from one or more other players before they can act or cooperate with other players to generate some pay-ofí. It is clear that such a permission structure limits the possibilities of cooperation. We derive a modified game that takes account of these limited cooperation possibilities. We then give axiomatic characterizations of the Shapley value of this modified game. '[n Gilles and Owen (1991) it is assumed that every player needs permission from nt teast one of his direct superiors. This is referred to as the Disjunctiue approach.

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